In the last few years there has been a dramatic increase in research
on economic geography -- that is, on where economic activity occurs and
why. This surge of interest has been driven to some extent by real-world
concerns -- the field has been given a big boost in particular by plans
to unify the European market, and the attempt to understand how this deeper
integration will work by comparing international economics within Europe
with interregional economics within the United States. But economic geography
has always been important; if it has been notably neglected by the economics
profession, this is not because economists have been uninterested in the
subject, but because they have regarded it as intractable. Their new willingness
to work on economic geography comes from their sense that new tools --
in particular, modeling tricks that have been developed to analyze industrial
organization, international trade, and economic growth -- have removed
crucial technical barriers, and transformed a once inhospitable field into
fertile ground for theorists.

The basic problem with doing theory in economic geography has always
been the observation that any sensible story about regional and urban development
must hinge crucially on the role of increasing returns. Suppose that we
really lived in the constant-returns world that is still assumed in much
economic theory. Then it would be hard to understand why the economy is
not characterized by "backyard capitalism", in which each household or
small group produces most items for itself. There would, admittedly, be
some unevenness in population density and some trade between locations
because of the variation in the natural environment: land differs in fertility,
while differences in soil, climate, and resources mean that no one locality
would produce all goods even under constant returns. Nonetheless, the dramatic
spatial unevenness of the real economy -- the disparities between densely
populated manufacturing belts and thinly populated farm belts, between
congested cities and desolate rural areas; the spectacular concentration
of particular industries in Silicon Valleys and Hollywoods -- is surely
the result not of inherent differences between locations but of some set
of cumulative processes, necessarily involving some form of increasing
returns, whereby geographic concentration can be self-reinforcing.

Unfortunately, increasing returns have always posed difficulties for
economic theorists. Except under very special circumstances they lead to
a breakdown of perfect competition; even if this problem can somehow be
finessed, they pose problems for the existence and uniqueness of equilibria.
For the theorist determined to make some headway in understanding the location
of economic activity, these difficulties have not been insurmountable.
For example, one can, like much of urban economics, simply take the existence
of cities (or central business districts within cities) as a given, and
trace out the consequences for land rents and land use; this is the basis
of the famous von Thünen model, which has given rise to a rich and
productive literature. Or one can, like urban systems theorists (above
all Henderson (1974, 1980, 1988)), represent increasing returns in a somewhat
black-box way as localized production externalities; this approach sidesteps
some important questions, but opens the door to a powerfully insightful
analysis of others. Still, until a few years ago these efforts remained
peripheral to the main body of economic theory, to such an extent that
most textbooks in economic principles still contain literally no reference
to the existence or role of cities and other geographic concentrations
of economic activity.

What has happened in the last few years is the emergence of a "new economic
geography" that is the fourth wave of the increasing returns revolution
in economics. The revolution began in the 1970s, in the field of industrial
organization, when theorists began for the first time to develop tractable
models of competition in the presence of increasing returns; in particular,
Dixit and Stiglitz (1977) developed a formalization of Chamberlin's concept
of monopolistic competition that, while admittedly a very special case,
has turned into the workhorse of theoretical modeling in a number of fields.
Beginning at the end of the 1970s, the analytical tools of the new industrial
organization theory were applied by a number of theorists to international
trade; a few years later the same tools were applied to technological change
and economic growth. In each case it was, of course, necessary to do much
more than mechanically apply the Dixit-Stiglitz model to the subject at
hand: new concepts needed to be developed, and at first there was a proliferation
of seemingly inconsistent models and approaches, in which each author appeared
to be inventing his or her own private language and notation. In time,
however, it became clear in each case that a core set of useful insights
had emerged; indeed, in retrospect it is remarkable how tightly integrated,
how classical in feel, both the "new trade" and "new growth" theory have
turned out to be.

Our sense is that the state of the "new economic geography" is currently
similar to that of the "new trade theory" circa 1984, or the "new growth
theory" circa 1990. That is, an exuberant and initially exhilarating growth
of theory has reached the point at which it has become difficult to see
the forest for the trees; and yet there is, if one looks for it, a strong
element of commonality among many if not all the analyses. The integration
of new trade and new growth theory was, we believe, powerfully aided by
the appearance of judiciously timed monographs that endeavored to synthesize
each field into a coherent whole: Helpman and Krugman's Market Structure
and Foreign Trade (1985), and Grossman and Helpman's Innovation
and Growth in the World Economy (1991). This book is, of course, an
effort to do the same with the new economic geography.

In the remainder of this chapter, we describe what we regard as the
unifying themes, methods, and questions of this new field, and set out
the plan of the book.

1.2 Linkages and circular causation

We would argue that the defining issue of economic geography is the
need to explain concentrations of population and/or economic activity --
the distinction between manufacturing belt and farm belt, the existence
of cities, the role of industry clusters. Broadly speaking, it is clear
that all these concentrations form and survive because of some form of
agglomeration economies, in which spatial concentration itself creates
the favorable economic environment that supports further or continued concentration.
And for some purposes -- as in the urban systems literature described in
Chapter 2 -- it may be enough simply to posit the existence of such agglomeration
economies. But the main thrust of the new geography literature has been
to get inside that particular black box, and derive the self-reinforcing
character of spatial concentration from more fundamental considerations.
The point is not just that positing agglomeration economies seems a bit
like assuming one's conclusion -- as a sarcastic physicist remarked after
hearing one presentation on increasing returns, "So you're telling us that
agglomerations form because of agglomeration economies". The larger point
is that by modeling the sources of increasing returns to spatial concentration,
we are able to learn something about how and when these returns may change
-- and then explore how the economy's behavior will change with them.

How should the returns to spatial concentration be modeled? More than
a century ago Alfred Marshall suggested a threefold classification. In
modern terminology, he argued that industrial districts arise because of
knowledge spillovers ("the mysteries of the trade become no mysteries,
but are as it were in the air"), the advantages of thick markets for specialized
skills, and the backward and forward linkages associated with large local
markets. While all three of Marshall's forces are clearly operating in
the real world, the new geography models have generally downplayed the
first two, essentially because they remain hard to model in any explicit
way. Instead, they have focussed on the role of linkages.

The linkage story is easy to tell if one is willing to be a bit vague
about the details. Producers, so the story goes, want to choose locations
that (i) have good access to large markets and (ii) have good access to
supplies of goods that they or their workers require. However, a place
that for whatever reason already has a concentration of producers will
tend to offer a large market (because of the demand generated by the producers
and their workers) and a good supply of inputs and consumer goods (made
by the producers already there). These two advantages correspond precisely
to the "backward linkages" and "forward linkages" of development theory.
Because of these linkages, a spatial concentration of production, once
established, may tend to persist -- and a small difference in the initial
economic size of two otherwise equivalent locations may tend to grow over
time.

Discussions of linkage-based spatial concentration that embody more
or less this story have been familiar to regional scientists for many years.
In Chapter 3 we describe in particular two such stories; the dynamic extension
of the base-multiplier approach largely identified with Pred (1966), and
the widely used concept of "market potential" associated with such authors
as Harris (1954). And provided that one is prepared to be strategically
sloppy about details, it is possible to jump straight from such stories
into heuristic models that are quite useful both for quick-and-dirty discussions
of real-world issues and as guides to the results of more careful modeling.
Such loose-jointed modeling is, we believe, under-appreciated in economics;
we try to give it its due.

Nonetheless, there are certain questions that traditional discussions
of linkages and economic geography do not address, yet become crucial once
one tries to get beyond the simplest stories. Most important of these is
the nature of competition. Linkage stories only work if there are increasing
returns in production at the level of the individual firm -- otherwise
the firm would not concentrate production where the market is largest,
but rather establish a separate facility to serve each market. But if there
are increasing returns, competition must be imperfect; how do firms compete
and set prices? Models like the base-multiplier story are also sloppy about
budget constraints -- it is unclear where all the money comes from or where
it goes. And in any story in which transportation costs play a crucial
role -- as they must in linkage stories about location, because otherwise
why does location matter? -- one must worry about how the resources used
in transportation fit into the picture.

The key enabling technology for the new economic geography has been
the development of a basic approach that deals in a consistent, if more
than a bit artificial, way with these problems -- together with an angle
of approach that allows theorists to cut through what might at first sight
seem be intractably complex problems of analysis.

We believe that the historical unwillingness of economists to address
issues of economic geography was mainly due to the sense that these issues
were technically intractable. As a result, we are only mildly apologetic
about the fact that our analysis depends crucially on what might perhaps
best be called modeling tricks -- assumptions that reflect not so much
a realistic view of how the world works as a judgement about what will
make the analysis of geographic issues manageable without doing too much
damage to the relevance of that analysis.

The first and biggest trick of our analysis is something we have in
common with the new trade and new growth literature: a heavy dependence
on the Dixit-Stiglitz model of monopolistic competition. To someone unfamiliar
with the exigencies of economic modeling, the popularity of the Dixit-Stiglitz
model might seem baffling. The model not only assumes that there are many
goods that, though constituting distinct products from the point of view
of consumers, also enter perfectly symmetrically into demand; it also assumes
that the individual utility function takes a particular, and fairly unlikely
form. Yet the Dixit-Stiglitz model has been the basis of a huge body of
economic theory in international trade, economic growth, and now economic
geography. Although we step away from that model on occasion, especially
in our more heuristic discussions, Dixit-Stiglitz assumptions are pervasive
in this book.

We are aware that this lends the analysis a certain air of unreality
-- that this book sometimes looks as if it should be entitled Games
You Can Play with CES Functions. Nonetheless, we regard the advantages
of the Dixit-Stiglitz model as overwhelming for our purposes. Essentially,
it is a way to respect the effects of increasing returns at the level of
the firm without getting bogged down in them. By assuming that those sectors
of the economy subject to increasing returns also satisfy the peculiar
assumptions of the Dixit-Stiglitz model, we are able to make sure that
we have represented market structure in an internally consistent way without
repeatedly going through a taxonomy of oligopoly models. Dixit-Stiglitz
also happens to lend itself naturally to general equilibrium analysis,
in which there are no loose ends about where money comes from and where
it goes. Above all, because Dixit-Stiglitz-type markets have a large number
of firms -- usually represented as a continuum -- we are able to reconcile
two seemingly incompatible goals: respecting the integer nature of individual
choices under increasing returns (each good will typically be produced
in only location) while representing the aggregate of such choices with
continuous variables (such as the share of production carried out in a
particular location). In short, Dixit-Stiglitz lets us have our cake in
discrete lumps while doing calculus on it, too.

Even with Dixit-Stiglitz, modeling a multi-location economy requires
some further funny but useful assumptions, which are distinctive to the
new economic geography (as opposed to the "new trade" or "new growth" literatures).
One key simplification is the assumption that transportation costs take
Samuelson's "iceberg" form: rather than modeling a separate transportation
sector, we suppose that a fraction of a good shipped simply melts away
or evaporates in transit. There turns out to be a tremendous synergy between
the assumption of iceberg transport costs and the Dixit-Stiglitz model,
in the sense that combining them causes many potentially nasty technical
complications simply to, well, melt away.

A bigger departure from the new trade and new growth literature comes
in our repeated use of a sort of evolutionary dynamics to make sense of
what are mainly static models. It is very hard to talk about economic geography
without using a language that suggests dynamic stories -- when one speaks
of a cumulative process by which spatial concentration reinforces
itself, one has a definite image of a snowballing urban or regional concentration,
developing over time. Yet to insist that models of economic geography explicitly
model firms and households as making intertemporal decisions based on rational
expectations would greatly complicate an already difficult subject. It
is very tempting to take a shortcut: to write down static models, then
impose
ad hoc dynamics on those models by, say, assuming that workers
migrate only gradually to locations that offer higher real wage rates --
and to use this ad hoc assumption to categorize some equilibria as stable,
others as unstable. We have systematically given in to this temptation.

This may require some further discussion. Ad hoc dynamics have been
very much out of fashion in economics for the past 25 years; dynamics are
supposed to emerge from rational, maximizing decisions by individual agents.
Yet what is one to do when a model predicts the existence of multiple equilibria,
as geography models usually do? Game theorists have wrestled with this
question, suggesting a variety of ways to "refine" the set of equilibria.
In recent years, they have increasingly come to accept the idea that it
is at least useful to try to assess the stability of equilibria by imagining
a process in which strategies become more or less prevalent over time based
on how well they perform -- in the same way that strategies followed by
organisms evolve under the pressure of natural selection. The funny thing
is that modern "evolutionary game theory" often looks quite a lot like
old-fashioned ad hoc dynamics. And indeed, the basic dynamic approach taken
in our first model (see Chapter 5) turns out to be identical to the "replicator
dynamics" now considered respectable among economic game theorists. (Game
theorists in biology, of course, regard the assumption that strategies
evolve myopically as a principle rather than a dubious shortcut). In short,
we believe that we are right to give in to the temptation to sort out equilibria
using simple, evolutionary dynamic stories, even though the models do not
ground these dynamics in any explicit decision-making over time.

Finally, even with all the special assumptions we have described, models
of economic geography can easily seem to be too complicated for paper-and-pencil
analysis. Yet if one is prepared to assign particular numbers to the parameters,
they can often be easily solved on the computer. A hallmark of the new
economic geography, as compared with the new trade and new growth literatures,
has been the willingness to turn where necessary to computer-assisted thinking:
to use high-tech numerical examples to guide and supplement analytical
results.

That said, in the course of working on this book we have found that
it is often possible to learn more from pencil and paper than one might
at first have thought. It often turns out that it is extemely useful to
start the analysis of a model by looking at numerical examples and simulations;
but that these numerical results then suggest the form of a solution that
can be derived in large part analytically. We are unabashed about the use
of the computer as an analytical tool; but this book has turned out to
have more analytical underpinning, and to be less reliant on purely numerical
results, than we expected.

1.4 The two questions

There are many questions one might ask about economic geography, and
we touch on a number of issues over the course of this book. We are, however,
able to stress the commonalities among a number of different models by
subjecting each model to one or both of two related but not quite identical
questions:

- When is a spatial concentration of economic activity sustainable?
(I.e., under what conditions are the advantages created by such a concentration,
should it somehow come into existence, sufficient to maintain it).

- When is a symmetric equilibrium, without spatial concentration,
unstable? (I.e., under what conditions will small differences among
locations snowball into larger differences over time, so that the symmetry
between identical locations will spontaneously break).

Or to put it differently, the first question asks whether the economy
can support something other than "backyard capitalism", whether backyard
capitalism is a necessary outcome; the second whether backyard capitalism
will automatically unravel, whether it is a possible outcome.

The answers to both of these questions hinge on the balance between
"centripetal" forces, forces that tend to promote spatial concentration
of economic activity, and "centrifugal" forces that oppose such concentration.
They are not quite the same question, however, essentially because the
first asks whether a situation is an equilibrium or not, and the second
asks whether an equilibrium is stable. Take, for example, the case of the
two-region model analyzed in Chapter 5. The first question asks whether,
if we simply posit that all manufacturing is concentrated in one region,
a worker who "defects" to the other region will find that doing so improves
his real wage; if it does, the concentration of manufacturing is not an
equilibrium. The second question asks whether, starting from an equilibrium
in which manufacturing is equally divided between the two regions, a movement
of a small number of workers from one region to the other will raise or
lower the relative wage in the destination region; if it raises it, the
symmetric initial situation will be unstable against small perturbations.

In the course of doing this book, we have discovered two important (and
surprising, at least to us) things about the two questions. First, although
the global behavior of new economic geography models is usually analytically
intractable, and must be explored via the computer, the answers to the
two questions can usually be reduced to closed-form expressions. That is,
we can derive explicit formulas for the "sustain point" at which an economy
with agglomeration becomes possible and the "break point" at which an economy
without agglomeration becomes unstable. (Doing so typically involves guessing
at the equilibrium, then confirming that guess, for the sustain point;
it involves linearizing the model around the symmetric equilibrium and
solving it in the case of the break point). These expressions reveal in
a clear way the role of backward and forward linkages in creating and sustaining
spatial concentration.

Second, across a variety of models that seem quite different on the
surface, a suitable redefinition of variables leads to the same
expressions for break point and sustain point. (This is particularly gratifying
in the case of the break point, because the equations are possible but
extremely annoying to solve; it is a great relief to find that this need
only be done once). In this sense we can claim to have developed a theory
of spatial concentration that is broader than any particular model, and
that helps us to see a number of different models as particular cases of
a more general approach.

It is not always useful to ask both questions. In some models there
is no sustain point -- although symmetry does break, the result is not
a full concentration of activity in one location. In the urban models of
Part III, on the other hand, the economic logic makes the question of symmetry-breaking
uninteresting; as we will see, it makes much more sense to posit the initial
existence of one or more cities, then evolve new cities by changing the
economy until that initial spatial pattern becomes unsustainable. Still,
since it is always useful to ask at least one of the questions and often
useful to ask both, we regard the two questions as one of the book's unifying
themes.

1.5 Plan of the book

The remainder of this book is in four parts.

Part I is a selective and analytical literature review. Our main concern
is with the long tradition of analysis in economic geography -- a tradition
that may have been neglected by the mainstream of economic theory, but
that nonetheless engaged in a process of cumulative development. We make
a somewhat artificial distinction between two parts of that tradition.
What we call "urban economics", surveyed in Chapter 2, consists mainly
of the von Thünen model, the attempt to explain cities by invoking
black-box agglomeration economies, and the use of those concepts in combination
in an urban systems theory that is different from but complementary to
much of what we try to do in this book. What we call "regional science"
(as a catchall for an eclectic mix of approaches that are at best loosely
modeled) is closer in spirit to the general approach of this book, trying
to derive spatial concentration from the interactions among economies of
scale, transportation costs, and factor mobility; in Chapter 3 we focus
on central-place theory, the dynamic base-multiplier model, and the concept
of market potential.

Part II introduces our basic approach in the context of "regional" models.
These are models in which a primary sector, "agriculture", is immobile
across locations, while "manufacturing", a sector subject to increasing
returns, can move between regions. Chapter 4 introduces the necessary technical
tools in the form of the Dixit-Stiglitz model. Chapter 5 then applies these
tools to a minimal model which shows how a two-region economy can become
differentiated between an industrialized core and an agricultural periphery;
the chapter offers a first, and relatively simple, illustration of how
numerical methods can be combined with analysis of the break and sustain
points to understand the economy's dynamics. Chapter 6 applies the same
basic approach to multi-region economies -- especially what we call the
"racetrack" economy, a stylized economy with a large number of locations
arrayed around a circle. We are able to get surprisingly clear results
about this multi-region economy using an approach originally suggested
by Alan Turing (1952) for the analysis of morphogenesis in biology; equally
surprisingly, the Turing analysis turns out to hinge on the same analysis
of symmetry-breaking that we applied in the 2-region case. Finally, both
Chapter 5 and Chapter 6 relied on a simplifying assumption that is very
unrealistic -- that agricultural goods can be transported costlessly. This
makes a difference; Chapter 7 explores the consequences of costly agricultural
transport.

Part III turns to a seemingly very different subject: the location of
cities in a world in which everything, including agriculture, is mobile.
Chapter 8 introduces the subject with a heuristic approach, in the spirit
of the "regional science" discussion in Chapter 3, that helps to provide
a guide to the more formal results. Chapter 9 develops a model that combines
a von Thünen-style approach to land rent with a linkage explanation
of manufacturing concentration, showing how a spatial pattern in which
a single city is surrounded by an agricultural hinterland can be self-sustaining
-- as long as the population is not too large. If the population does become
too large, it will be in the interest of a small group of workers to move
to some other location; so by using the criterion of sustainability, it
is possible to develop a model of the emergence of new cities and hence
of a multi-city structure, a task carried out in Chapter 10. If one then
supposes that there are actually several manufacturing industries, with
different costs of transportation and/or economies of scale, the process
of city formation can yield a hierarchy of cities of different types and
sizes, as shown in Chapter 11. Chapter 12 takes a break from the main line
of argument to discuss the striking and puzzling empirical regularities
that characterize actual urban hierarchies. Chapter 13 then returns to
the main line of argument to show how variations in the natural landscape,
such as ports and rivers, can influence urban location.

Part IV of the book, finally, turns to the analysis of international
trade -- defined in this case as models in which labor is immobile between
locations. What we do here, however, is to introduce the possibility that
labor can move between agriculture and manufacturing, and assume that manufacturing
firms use each others' outputs as intermediate inputs. What Chapter 14
shows is that this setup yields backward and forward linkages that can
produce symmetry-breaking in exactly the same way that the movement of
labor does in the core-periphery model; in this case, however, the breaking
and restoration of symmetry drives international inequalities in wages.
That model suggests that the secular decline in transport costs can explain
both the initial division of the world into industrial and nonindustrial
regions, and the more recent spread of manufacturing to newly industrializing
economies. Chapter 15 offers an alternative explanation of that spread,
focussing instead on the effects of market growth. Chapter 16 turns to
the sources of international specialization within the manufacturing
sector. Chapter 17, paralleling Chapter 6, offers an analysis of international
trade without countries - that is, of the emergence of regions of specialization
in a borderless world with continuous space. Finally, Chapter 18 examines
a possible interaction between international trade and the process of urbanization
within nations.

What we find remarkable and gratifying in all of this is the extent
to which we are able to use the same basic modeling "architecture" to address
so many issues in seemingly disparate fields. But then our point is precisely
that these fields are not that disparate after all: be it urban economics,
location theory, or international trade, it's all about where economic
activity takes place - and why.